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Driven particles at fluid interfaces acting as capillary dipoles

Published online by Cambridge University Press:  30 March 2015

Aaron Dörr*
Institute for Nano- and Microfluidics, Center of Smart Interfaces, Technische Universität Darmstadt, Alarich-Weiss-Straße 10, 64287 Darmstadt, Germany
Steffen Hardt
Institute for Nano- and Microfluidics, Center of Smart Interfaces, Technische Universität Darmstadt, Alarich-Weiss-Straße 10, 64287 Darmstadt, Germany
Email address for correspondence:


The dynamics of spherical particles driven along an interface between two immiscible fluids is investigated asymptotically. Under the assumptions of a pinned three-phase contact line (TCL) and very different viscosities of the two fluids, a particle assumes a tilted orientation. As it moves, it causes a deformation of the fluid interface which is also computed. The case of two interacting driven particles is studied via the linear superposition approximation. It is shown that the capillary interaction force resulting from the particle motion is dipolar in terms of the azimuthal angle and decays with the fifth power of the inter-particle separation, similar to a capillary quadrupole originating from undulations of the TCL. The dipolar interaction is demonstrated to exceed the quadrupolar interaction at moderate particle velocities.

© 2015 Cambridge University Press 

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